Jeremy Hunt has again been accused of having too close links to private healthcare after it emerged that he is in talks to hire a personal adviser from the sector as one of his first moves as health secretary.

Hunt is lining up Christine Lineen, formerly head of communications at Circle Health, the controversial firm which earlier this year became the first to run an NHS hospital, to become one of his policy experts.

The move was seized on by shadow health minister Jamie Reed as a sign that the new health secretary has an agenda of opening up the NHS to private healthcare firms.

The former culture secretary has already been criticised after the Observer revealed how he had personally intervened to ensure that Virgin Care was able to take over the running of seven community hospitals in his constituency.

Hunt, who replaced Andrew Lansley in the cabinet reshuffle, was so concerned by a delay to the £650m deal earlier this year that he asked for assurances from NHS Surrey officials that it would be swiftly signed. Virgin Care, which is part-owned by Sir Richard Branson's Virgin Group, subsequently agreed on a five-year contract in March.

Reed said the prime minister's decision to appoint Hunt, who many believed was lucky to stay in government following the row over his relationship with Rupert Murdoch's News Corp, reinforced fears over the "NHS privatisation agenda". He added: "The whole country should be worried by the cosy relationship between the Tories and private healthcare – there is clearly a revolving door between them and it leads right to the heart of government."

Lineen worked as a special adviser to Lansley, the author of the NHS reforms designed to open the service to the third sector, before moving two years ago to Circle Health.

The company, run by a former Goldman Sachs banker, was awarded management of Hinchingbrooke hospital in Cambridgeshire last year in a ground-breaking move lauded by ministers as a "good deal for patients and staff".

It is owned by companies and investment funds registered in the British Virgin Islands, Jersey and the Cayman Islands in an arrangement which allows investors to avoid tax on their shares.

Circle's controversial takeover of Hinchingbrooke hospital came despite admissions in a document to the stock exchange that patient care could suffer under its plans to expand its empire and seek profit from the health service.

Circle Health said it was already feeling a strain on resources due to its aggressive business strategy, and the firm's ambition to further expand into the NHS "could affect its ability to provide a consistent level of service to its patients. A Department of Health spokesman said "no decision has yet been taken".